For the single-particle potential surface of the two-center shell model, two geometrical quantities which determine the local Liapunov exponents are derived. It is shows that the appearance of a large positive local Liapunov exponent in a large area of the coordinate space leads to the quantum chaotic motion of a single particle in heavy nuclei. For both small and large (or medium) separations of the two centers, the dependence of the quantum chaotic motion on the neck deformation is interpreted from the dynamical point of view.